Path-dependent infinite-dimensional SDE with non-regular drift : an existence result

IF 1.2 2区 数学 Q2 STATISTICS & PROBABILITY
D. Dereudre, S. Roelly
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引用次数: 7

Abstract

We establish in this paper the existence of weak solutions of infinite-dimensional shift invariant stochastic differential equations driven by a Brownian term. The drift function is very general, in the sense that it is supposed to be neither small or continuous, nor Markov. On the initial law we only assume that it admits a finite specific entropy. Our result strongly improves the previous ones obtained for free dynamics with a small perturbative drift. The originality of our method leads in the use of the specific entropy as a tightness tool and on a description of such stochastic differential equation as solution of a variational problem on the path space.
具有非规则漂移的路径相关无限维SDE:一个存在性结果
本文建立了布朗项驱动的无限维移不变随机微分方程弱解的存在性。漂移函数是非常通用的,因为它既不是小函数,也不是连续函数,也不是马尔可夫函数。在初始定律上,我们只假定它具有有限的比熵。我们的结果大大改进了先前在小微扰漂移下得到的自由动力学结果。我们的方法的独创性在于使用比熵作为紧性工具,并将这种随机微分方程描述为路径空间上变分问题的解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
2.70
自引率
0.00%
发文量
85
审稿时长
6-12 weeks
期刊介绍: The Probability and Statistics section of the Annales de l’Institut Henri Poincaré is an international journal which publishes high quality research papers. The journal deals with all aspects of modern probability theory and mathematical statistics, as well as with their applications.
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